On the linear orthobaric-density representation of near-critical solvation quantities what can we conclude about the accuracy of this paradigm?

Abstract In this work, we have derived rigorous expressions for the thermodynamic description of the solvation behavior of a model solute in highly-compressible environments of a real solvent, in order to address the question posed in the title of this manuscript. Toward that end, we first provide the essential statistical thermodynamic foundations to support a fundamentally-based approach for the determination of the Krichevskii parameter of a solute in any solvent, based solely on the knowledge of the corresponding Henry's law constant. Second, we analyze the actual orthobaric-density behavior of ln Q ( T , P σ ) and T σ ln Q ( T , P σ ) , when Q = K D ∞ and Q = ( H i , j I S / f j o ) , for an infinitely dilute ideal gas solute in an aqueous solution, a system for which we have complete knowledge of its microscopic and thermodynamic behaviors. Third, we invoke these results to test the assumptions behind the modeling of the orthobaric-density dependence of the Henry's law constant, infinite dilution vapor-liquid distribution, and Ostwald coefficients of real solutes. Fourth, we discuss the implications underlying the interpretation of the regressed orthobaric-density slopes, the accuracy of the resulting effective Krichevskii parameters, and the extension of the current analysis to the orthobaric-density behavior for the corresponding Ostwald coefficient, T σ ln L i , j ∞ ( T , P σ ) . Finally, we show how the fundamentally-based orthobaric-density linear expressions of ln Q ( T , P σ ) for the three Q − quantities converge to the corresponding, empirically-found, T σ ln Q ( T , P σ ) asymptotic linear representations for near-critical infinitely dilute solutions.